Except for a few special states, computing quantum discord remains a complicated optimization process. In this paper, we present analytical solutions for computing quantum discord of the most general class of X -states and the criteria for each analytical solution to be valid. We discuss parameter regions that correspond to different analytical solutions and explain the underlying reasons for such structure to exist. We apply our formalism to study both arbitrary X -states and X -states with certain symmetries. We find that our analytical formalism is in excellent agreement with numerical calculation of quantum discord in both cases.

Due to COVID-19, university students continued their academic training remotely. To assess the effects of emergency remote teaching (ERT), we evaluated the expectations and, subsequently, the experiences of university students about online education. This study employed a simple prospective design as its method. We assessed the expectations of 1,904 students from different discipline areas (1,106 women and 798 men; age M = 21.56; SD = 3.07) during the beginning of the first semester, March 2020 (T1), and their experiences at the end of the same academic period, September 2020 (T2). We used convenience non-probability sampling. Participants responded to the questionnaire on Expectations toward virtual education in higher education for students and the questionnaire on virtual education experiences in higher education. The results showed that students’ responses reflected low expectations regarding peer relationships and comparison with face-to-face education (T1). This perception was maintained during the evaluation of experiences (T2). Students reported positive experiences regarding online teaching and learning, online assessment, and their self-efficacy beliefs at T2. Statistically significant differences between measurements were found, with the expertise presenting higher averages than expectations. Furthermore, differences by gender were identified, reporting a positive change in the scores of women. In addition, results reflected differences according to the disciplinary area, showing Social Sciences and Medical and Health Sciences students a more significant size effect. Findings regarding the empirical evidence and the implications for future teaching scenarios in Higher Education are discussed.

Due to the COVID-19 pandemic, students worldwide have continued their education remotely. One of the challenges of this modality is that students need access to devices such as laptops and smartphones. Among these options, smartphones are the most accessible because of their lower price. This study analyzes the usage patterns of smartphone users of undergraduate Science, Technology, Engineering, and Math (STEM) students during the COVID-19 pandemic. This cross-sectional descriptive study included 365 students: 162 (44.4%) women and 203 (55.6%) men from a Chilean university. The results revealed that students often accessed the learning management system (LMS) with their computers rather than with their smartphones. Students were connected to the LMS for more hours on their computers than on their smartphones. However, they spent more hours simultaneously connected on their computers and smartphones than just on their computers. During the day, students accessed the LMS mainly from 13:00 to 1:00. The number of connections decreased from 1:00 to 8:00 and increased from 8:00 to 13:00. The LMS resource that students accessed the most using smartphones was discussion forums, while the one they accessed the least was wiki pages. We expect these results to motivate faculties to schedule their activities during the hours students tend to be online and promote discussion forums.

Due to the closure of universities worldwide because of the COVID-19 pandemic, teaching methods were suddenly transformed to an emergency remote teaching (ERT) modality. Due to the practical nature of STEM courses, students cannot participate in activities in which manipulating objects is necessary for accomplishing learning objectives. In this study, we analyze the relation among STEM students learning beliefs at the beginning of ERT (T1) with their Learning Management systems (LMS) time-on-task and their final academic performance (T2) during the first semester of ERT. We used a prospective longitudinal design. 2063 students (32.3% females) from a university in Chile participated, where the academic year starts in March and finishes in December 2020. We assessed their learning and performance beliefs through an online questionnaire answered at the beginning of the academic period (T1). Then, using learning analytics, time invested in the CANVAS LMS and the academic performance achieved by students at the end of the semester (T2) were assessed. The results show that students mainly stated negative beliefs about learning opportunities during ERT (n = 1,396; 67.7%). In addition, 48.5% (n = 1,000) of students stated beliefs of “medium” academic performance for the first semester (T1). Students with lower learning beliefs at T1 spent less time in the LMS during the semester and had a lower academic performance at T2 than students who had higher learning beliefs at T1. The implications of these findings on the role of instructors and institutions of higher education are discussed.

Due to COVID-19, universities have been facing challenges in generating the best possible experience for students with online academic training programs. To analyze professors' expectations about online education and relate them to student academic performance during the COVID-19 pandemic, and considering the socio-demographic, entry, and prior university performance variables of students. A prospective longitudinal design was used to analyze the expectations of 546 professors (54.8% male) in T1. In T2, the impact of the expectations of 382 of these professors (57.6% men) was analyzed, who taught courses during the first semester to a total of 14,838 university students (44.6% men). Professors' expectations and their previous experience of online courses were obtained during T1, and the students' academic information was obtained in T2. A questionnaire examining the Expectations toward Virtual Education in Higher Education for Professors was used. 84.9% of the professors were considered to have moderate to high skills for online courses. Differences in expectations were found according to the professors' training level. The professors' self-efficacy for online education, institutional engagement, and academic planning had the highest scores. The expectations of professors did not directly change the academic performance of students; however, a moderating effect of professor's expectations was identified in the previous student academic performance relationship on their current academic performance.

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We put the pure-state decomposition mathematical property of a mixed state to a physical test. We begin by characterizing all the possible decompositions of a rank-two mixed state by means of the complex overlap between two involved states. The physical test proposes a scheme of quantum state recognition of one of the two linearly independent states which arise from the decomposition. We find that the two states associated with the balanced pure-state decomposition have the smaller overlap modulus and therefore the smallest probability of being discriminated conclusively, while in the nonconclusive scheme they have the highest probability of having an error. In addition, we design an experimental scheme which allows to discriminate conclusively and optimally two nonorthogonal states prepared with different a priori probabilities. Thus, we propose a physical implementation for this linearly independent pure-state decomposition and state discrimination test by using twin photons generated in the process of spontaneous parametric down conversion. The information-state is encoded in one photon polarization state whereas the second single-photon is used for heralded detection.

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